Puljujärvi played in the 2011 Quebec International Pee-Wee Hockey Tournament with the Finland Selects youth team. Puljujärvi began his hockey career and Fin-Jr. league debut in 2013–14 with the Kärpät Jr. hockey team. In the two seasons he participated in, Puljujärvi recorded 23 points in 18 games and 18 points in 11 games. Puljujärvi made his Liiga debut playing with Kärpät during the 2014–15 Liiga season. Leading up the NHL draft, he was ranked as the number three European skater. He was described as a big, mobile, skilled, an all-around winger who can score and pass. Puljujärvi was sent down mid-season and made his Mestis debut in 2014–15 with Kärpät affiliate Kajaanin Hokki. He finished the season with 13 points in 15 games. During the season, Puljujärvi was considered good enough again, that he was sent to the Kärpät hockey team to continue his career there. Kärpät would be his final team before he would be drafted into the NHL. In 2015–16, his first full season with Kärpät, Puljujärvi played in 50 Liiga games, scoring 28 points, as well as in ten playoff games with four goals and five assists. He also competed in the Champions Hockey League with the club, recording 2 assists in 13 games but remained goalless. Puljujarvi would then leave the team and European hockey altogether, as he would be drafted into the NHL as the fourth overall pick by the Edmonton Oilers. He returned to Kärpät in August 2019, signing a one year contract, though the Edmonton Oilers maintain his NHL rights.
Edmonton Oilers
Puljujärvi signed a three-year, entry-level contract with the Edmonton Oilers on 13 July 2016. He opted to wear sweater #98 with the team, making him the first NHL player to do so since 1985, when Brian Lawton wore the number in a regular season game. After making the Oilers opening night roster for the 2016–17 season, he made his NHL debut on opening night with the Oilers in which he scored his first career NHL goal on 12 October 2016. After just 28 games, Puljujärvi was sent down to the Oilers' American Hockey League, the affiliate Bakersfield Condors, for more development time. During his tenure at the AHL, Puljujärvi was able to score 12 goals and 16 assists in 39 games. Puljujärvi returned to the Oilers in the 2017 NHL pre-season. In his best game so far for the Oilers, Puljujärvi scored two goals and an assist to help the Oilers extend their winning gap against the Winnipeg Jets. Because of Puljujärvi's pre-season rout, he was selected to take the first line position along with Patrick Maroon and Connor McDavid, beginning at the Edmonton Oilers–Carolina Hurricanes pre-season game. Puljujärvi would then retake the fifth line, but would eventually be sent down to the Condors once again for more development. He was put back on the Oilers lineup on 10 November 2017, replacing Anton Slepyshev, who was injured at the time. On 20 January 2018, Puljujärvi registered a career-high three-point game, recording one goal and two assists against the Vancouver Canucks. This would also mark the first time Puljujärvi received a first star for a game.
Puljujärvi was born to Finnish parents in Sweden and lived there until he was four, though culturally, he identifies as Finnish. He holds both Finnish and Swedish citizenship. In his free time, he also likes playing ice hockey with neighbourhood kids.